Question

Why is \(0 \times 0 \) not \(\text{undefined}\)? How can we multiply nothing to nothing?

Answer 1

\(0 \times 1\), on the other hand, can be calculated by adding 0 to itself once, which leaves 0.
Same for all other \(0 \times n\) where \(n\) is not zero.

Answer 2

How can we add 0 to itself no number of times?

Answer 3

0=1-1
0*0=0*(1-1)=0-0=0

Answer 4

zero is an approximation anyway.

Answer 5

There still can be mathematical fallacy in any proof, @apple-pi.